Problems with Texturing in Blender Game Engine
Judging by the images you posted, this is probably what's wrong with you scene.
Flipped normals

Steps to fix:-

1. Select your object and go to edit mode
2. Move over to the shadings and UV tab
3. Select everything in your mesh
4. Click on recalculate



5. Go to properties panel and find the shading section and turn off Backface culling

Explanation:-

What Backface culling does is cull or clip the back sides of the face, and the back side is determined by the normals. Your model, judging from the picture, has its normals flipped inside out, and you have backface culling on therefore it's culling all the backfaces. If recalculation does not work, then it means some of the faces are flipped unevenly, thus they need to be manually flipped by using the Flip Direction button in the same shading panel in the tools tab region.